Percentage error in the measurement of time period of a pendulum if maximum error in

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1.Units, Dimensions and Measurement

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What is the percentage error in the measurement of time period of a pendulum if maximum error in the measurement of $l$ and $g$ are $2\%$ and $4\%$ respectively .......... $\%$

A

$6$

B

$4$

C

$3$

D

$5$

Solution

$\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$

$\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{1}{2} \frac{\Delta \ell}{\ell}+\frac{1}{2} \frac{\Delta \mathrm{g}}{\mathrm{g}}$

$=\frac{1}{2} \times 2+\frac{1}{2} \times 4$

$=1+2=3 \%$

Standard 11

Physics

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